The Research On Parallel Algorithms Of 2-D Shallow Water Equations

The high order and high resolution finite volume method is a conservative high-performance algorithm scheme on unstructured grids. It is being used to solve the numerical calculating of shallow water equation more and more. Based on it, the parallel computing of 2-D shallow water equations was researched.The parallel computing is one of the most effective ways to improve the calculating speed at present. Some fundamental knowledge of parallel computing was introduced, programming models, programming methods, programming patterns and so on which is involved in parallel programming were described.Lenovo cluster was introduced as the physical platform of the study. Also, the calling method, parameter explaining of the usual interface in MPI which is a library used with the FORTRAN language were given out. The performance of parallel computing was influenced by the communication directly. Mainly, the point-to-point communication and the collective communications were presented.To solve the 2-D shallow water equations, the numerical model which adopted the high order and high resolution finite volume method on unstructured grids was introduced.Domain decomposition algorithm is one of the most important schemes in parallel computing. About the decomposition of unstructured grids, a mathematicalmodel (MMET) has been built, which minimizing the maximum execution time ofsub-domains was made as objective function. Then, an algorithm was designed for this model. By calculating, a good speedup and efficiency were achieved. At the basis of the algorithm, a new algorithm was given out. Using the new one, the advantage of the new algorithm on computing result and computing efficiency was approved, especially on computing efficiency.About the domain decomposition of unstructured grids, the MMET model was adopted. After the domain decomposition, the data were pre-handled for parallel computing. Parallel programming was designed on the basis of serial programming by using peer-to-peer mode and standard communication mode. Finally, the serial programming which has been programmed for simulating of the tidal bore in Qiantang Estuary which adopted the high order and high resolution finite volume method was parallelized on the Lenovo cluster.